From Hard Drop - Tetris Wiki

Back-to-Back T-spin Triple is a difficult maneuver in some SRS based games, which in (for example) Tetris DS sends a total of thirteen garbage rows to the opponent. It requires the player to make two T-Spin Triple line clears back-to-back. See Infinite TST for a loop where each time 2 T-Spin Triples are stacked above each other like described in this article.

Setups notched on side

LT/JT

LT/JT is the simplest set up. Its flaw is its heavy dependence on T tetrominoes, which could otherwise be held to complete the T-spin.

TLTL

JTJT

TLJT

JTTL

Setups involving S and I

LSIL

JZIJ

S/Z Core Replacement

The core of LT/JT can be replaced with two S or Z tetrominoes:

JSSL

JZZL

TIOT

JZTT

OZJ Setup

OZJ is arguably the safest and most efficient BtB T-Spin Triple setup. The setup is special in that it takes the least amount of tetrominoes to set up the notch. The player is also given 7 columns of space to stack freely. Perhaps the most unique aspect of this setup lies in the fact that one of the T-Spin Triples can be turned into a T-Spin Double by placing an I into the empty column, a scapegoat for ill-fated garbage. This must be done before the final "lid" piece has been placed at the top of the setup. As an extra bonus, the overhang left over from a complete OZJ can be transferred into a Double Triple 2 setup. In practice, planning the stacking is required to set up DT2 correctly, or blocks will get in the way. The ZZJ variation is useful for S/Z starts.

OZJ

I Abort (requires L/J spin triple, double overhang and 180° rotation

DT2 Transfer

ZZJ Setup

ZZJ

Overhang left over

Cleaned up with a slide (useful for tetrises)

Or twist

JZJ Setup

This setup has a T-Spin Double bonus and no overhang to clean up afterward.

JZJ

T-Spin Double bonus

Done

Setups notched in center

Setups containing I:

JILS

IIS

IIJ

Mirror possible: (IO)

Switching sides

A player may switch sides to clear Back to Back T-spin Triples indefinitely.

Any T-spin line clear is good enough to keep the "Back to Back" alive, which allows for lopsided designs.

These two have interchangeable parts.

Back-To-Back-To-Back

Simple additions to patterns can lead to more than 2 T-Spin Triples:

Stacking JT/TL

OZJ Enhanced

4 TST's

LSOZJ

5 TST's

TJLSOZJ

Imperial Cross Cannon

When building the other side, leave a notch in the bottom TST to turn it into an Imperial Cross.